Early Posting

Accepted papers to appear in an upcoming issue

Optica Publishing Group posts prepublication articles as soon as they are accepted and cleared for production. See the FAQ for additional information.

A HDR Vision Sensor with Neuro-Memristive Skin Detection for Edge Computing

Francesco Paissan, Michela Lecca, Roberto Passerone, Elisabetta Farella, and Massimo Gottardi

DOI: 10.1364/JOSAA.516912 Received 27 Dec 2023; Accepted 12 Apr 2024; Posted 12 Apr 2024  View: PDF

Abstract: Human skin classification is an essential task for several machine vision applications such as human-machine interfaces, people/object tracking, and classification. In this paper, we describe a hybrid CMOS/memristor vision sensor architecture embedding skin detection over a wide dynamic range. In-sensor RGB to rg-chromaticity color space conversion is executed on the fly through a pixel-level automatic exposure time control. Each pixel of the array delivers two pre-filtered analog signals, the r and g values, suitable for being efficiently classified as skin or non-skin through an analog memristive Neural Network (NN), without the need for any further signal processing. Moreover, we study the NN performance and theorize how it should be added in the hardware. The skin classifier is organized in an array of column- level memristor-based NN to exploit the nano-scale device characteristics and non-volatile analog memory capabilities, making the proposed sensor architecture highly flexible, customizable for various use-case scenarios, and low-power. The output is a skin bitmap that is robust against variations of the illuminant color and intensity.

Autofocusing in digital holography based on adaptive genetic algorithm

Zhongyang Wang, Hong-wei Ma, Yuan Chen, and Dengxue Liu

DOI: 10.1364/JOSAA.518105 Received 23 Jan 2024; Accepted 11 Apr 2024; Posted 11 Apr 2024  View: PDF

Abstract: In digital holography (DH), determining the reconstruction distance is critical to thequality of the reconstructed image. However, traditional focal plane detection methods requireconsiderable time investment to reconstruct and evaluate holograms at multiple distances. Toaddress this inefficiency, this paper proposes a fast and accurate autofocusing method based onan adaptive genetic algorithm. This method only needs to find several reconstruction distancesin the search area as an initial population, and then adaptively optimize the reconstructiondistance through iteration to determine the optimal focal plane in the search area. In addition,an off-axis digital holographic optical system was used to capture the holograms of the USAFresolution test target and the coin. The simulation and experimental results indicated that,compared with the traditional autofocusing, the proposed method can reduce the computationtime by about 70% and improve the focal plane accuracy by up to 0.5mm.

Polarization structure of optical vortices in inclined Laguerre-Gaussian beams passed through a uniaxial crystal

Yuriy Egorov and Aleksandr Rubass

DOI: 10.1364/JOSAA.523057 Received 05 Mar 2024; Accepted 11 Apr 2024; Posted 11 Apr 2024  View: PDF

Abstract: The work shows that in linearly polarized Laguerre-Gaussian beams passing through an anisotropic medium at an angleto the optical axis of the crystal, the distribution of optical vortices is devoid of axial symmetry. It is shown that thetrajectories of movement of polarization singularities in the plane of the Laguerre-Gauss beam are different for differentcases of input linear polarization at angles 45o g = ± and there is an exchange of optical vortices, provided that the signof the topological charge is preserved. It is shown that when the axis of an anisotropic medium is tilted, the movement ofoptical vortices occurs, accompanied by topological reactions of creation, destruction, or displacement of opticalvortices to the periphery of the beam. It is characteristic that at angles of inclination by linear polarization 45og= +,topological reactions of creation and annihilation occur, and at angles 45o g = - , topological reactions of displacement ofoptical vortices to the periphery of the beam occur.

High-Efficiency Scattering Field Modeling in Metallic Components: A Machine Learning-Inspired Approach

Po-Jui Chiang, CHIH-LUNG TSENG, and Chien-Kun Wang

DOI: 10.1364/JOSAA.507016 Received 27 Sep 2023; Accepted 09 Apr 2024; Posted 11 Apr 2024  View: PDF

Abstract: We present a highly efficient method for characterizing the scattering field distributionof surface plasmon polaritons in metallic components by combining the eXtended PseudospectralFrequency-Domain (XPSFD) method with an iterative, machine learning-inspired procedure.Shifting away from traditional matrix operations, we utilize the ’Adam’ optimizer—an effectiveand swift machine learning algorithm—to solve the scattering field distribution. Our methodencompasses the derivation of the associated cost function and gradient differentiation of the field,leveraging spectral accuracy at Legendre collocation points in the Helmholtz equation. We refinethe total-field/scattered-field (TF/SF) formulation within the XPSFD framework for optimizedincident field management, and employ Chebyshev-Lagrange interpolation polynomials for rapid,accurate computation of broad-band results. To ensure global accuracy, we introduce uniquephysical boundary conditions at subdomain interfaces. Demonstrating our method’s robustnessand computational efficiency, we model perfect electric conductors (PEC) and silver nanocylinders,and apply our approach to analyze the excited electric field on subtly distorted metallic surfaces,particularly plasmonic structures, thereby validating its wide-ranging effectiveness.

Time characteristics of aero-optical imaging degeneration of ellipsoidal dome under variable operating conditions

Jiaqian Yu, Chonghui Zhu, and song long

DOI: 10.1364/JOSAA.515243 Received 13 Dec 2023; Accepted 09 Apr 2024; Posted 10 Apr 2024  View: PDF

Abstract: As the missile flies at high speed, the index and surface shape of the conformal dome will vary under the influence of theaero-optical effect, which will degenerate the performance of the seeker’s imaging detection system. However, manyprevious studies on aero-optical imaging deterioration of optical domes are usually carried out under fixed operatingconditions, which are not in line with the real flight scene of the missile. Besides, the aero-optical imaging degenerationof the dome is diverse as the flight time increases. Therefore, it is of great significance to study the time characteristics ofaero-optical imaging degradation of optical domes under variable work conditions. In this study, taking an air-to-airmissile as an example, the Zernike polynomials, wavefront aberration, Strehl ratio, and image simulation are applied toevaluate the aero-optical imaging deterioration of an ellipsoidal dome in the flight time range of 0-10 s under variableworking conditions. The simulation results show that, as the flight time increases, (1) the dynamic range of tilt, defocus,astigmatism, coma, and wavefront aberration increase; (2) the Strehl ratio and the peak signal-to-noise ratio (PSNR) ofthe simulated images decrease. Therefore, the influence of flight time on the aero-optical image degradation of theellipsoidal dome is gradually serious.

Saturation of anisoplanatic error in Kolmogorov and non-Kolmogorov turbulence

Jeremy Bos

DOI: 10.1364/JOSAA.520981 Received 07 Feb 2024; Accepted 05 Apr 2024; Posted 08 Apr 2024  View: PDF

Abstract: This work explores the conditions resulting in saturation of angular anisoplanatic error. When turbulence ismodeled with a von Kármán outer scale or when piston and aperture tilt are compensated the anisoplanaticerror can saturate to less than one squared radian. In Kolmogorov turbulence anisoplanatic error is limitedto values smaller than one when the ratio of the Fried parameter to the outer scale is 0.349. To understandthe effect of compensation on saturation both a first-order asymptotic approach and numerical integrationare considered for both plane and spherical wave sources and in non-Kolmogorov turbulence. Asymptoticexpressions are found to agree with the numerical results as long the ratio of outer scale to aperture size isless than five. For a plane wave propagating in Kolmogorov turbulence, the compensated anisoplanaticerror is found to saturate when D/r0 = 3.9 when the outer scale is equal to the aperture size. When aspherical wave source is considered D/r0 increases to 5.8; as expected these values are related by a factor of1.8. This work also formulates the anisoplanatic error in terms of an integrated strength parameter and themean turbulence height allowing extension to arbitrary path geometries and power law exponents. Usingthis approach I find smaller power law exponents increase the mean turbulence height thereby decreasingthe isoplanatic angle; the opposite applies as the power law exponent is increased relative to Kolmogorovturbulence.

Performance Evaluation and Comparative Research of Underwater Wireless Optical Communication System by Using Different Structured Beams

Shuang He, Peng Zhang, Hao Yu, Dongsheng Tian, Hang Chen, Hui Dai, Pengfei Ye, Dashuai Wang, and Shoufeng Tong

DOI: 10.1364/JOSAA.517901 Received 09 Jan 2024; Accepted 05 Apr 2024; Posted 05 Apr 2024  View: PDF

Abstract: Structured beams have attractedincreasing interest in free-space and fiberbased optical communications.Underwater wireless opticalcommunication (UWOC) is becoming aprospective technique in marineexploration. We investigated UWOCperformance using different representativestructured beams. The transmissionperformances of the Gaussian, BesselGaussian (BG), Ince-Gaussian (IG), andradially polarized Gaussian (RPG) beamswere experimentally demonstrated andevaluated in underwater channelssubjected to thermal gradient. Theexperimental results show that the BG, IG,and RPG perform better against thethermal gradient. Compared with theGaussian beams, the beam wanders of BG,IG, and RPG beams under the thermalgradient have been reduced by 56.9%,8.2% and 59%, the scintillation indiceshave been decreased by 12.8%, 17.3% and28.9%, and the BER performance of theBG, IG and RPG beams have beenimproved by ∼5.5 dB, ∼3.7 dB, and∼ 5.2dB at the forward error correctionthreshold (FEC threshold). Based on theabove results, the RPG beam is a morepromising light source for UWOC. Theexperimental results provide a promisingbeam choice for UWOC.

Randomness of Optical Turbulence Generated by Rayleigh-Bénard Convection using Intensity Statistics

Nathaniel Ferlic, Svetlana Avramov-Zamurovic, Owen O'Malley, Thomas Kelly, and Kyle Judd

DOI: 10.1364/JOSAA.520909 Received 07 Feb 2024; Accepted 03 Apr 2024; Posted 05 Apr 2024  View: PDF

Abstract: The experimental study of optical turbulence provesdifficult due to challenges in generating controllableconditions in a laboratory environment. Confined water tanks that produce Rayleigh-Bénard (RB) convectionare one method to generate optical turbulence using acontrollable temperature gradient. It is of utmost concern to quantify the properties of the optical turbulencegenerated for characterization of other optical applications such as imaging, sensing, or communications. Inthis experimental study a Gaussian beam is propagatedthrough a RB water tank where two intensity measurements are made at the receivers pupil and focal plane.The pupil and focal plane results include quantificationof the intensity fluctuation distribution, scintillationdistribution, and refractive index structure constant atvarious values of the temperature gradient. The angleof arrival fluctuations are also calculated at the focalplane to obtain a second estimate of C2n. Comparisonof the pupil plane estimate for C2n using scintillationindex and focal plane angle of arrival fluctuations arecompared to preliminary predictions of C2n as a functionof RB temperature gradient showing C2n ∼ ∆T4/3. Theoutcomes of the study confirm that the RB process produces intensity fluctuations that follow gamma-gammaand log-normal probability density functions. Estimatesof the refractive index structure constant C2n produce thesame trends with different magnitudes when measuredfrom the pupil and focal plane.

Strong multiperiod forerunning light jet within a double prism gap: A counterintuitive manifestation of causality

Alexander Turchin and Mikhail Vasnetsov

DOI: 10.1364/JOSAA.516563 Received 27 Dec 2023; Accepted 02 Apr 2024; Posted 02 Apr 2024  View: PDF

Abstract: We report on the effect of a strong and protractedadvanced response in pulse transmission and reflectionin a double-prism scheme. In distinction to the wellknown activity on superluminal-like tunneling of anelectromagnetic pulse through a gap of a double prism,we consider an optical pulse refracting to a gap andsliding therein. The formation of multiperiod light jetrunning within the gap well before the incident pulse isshown with account of normal material dispersion andexcitation of leaky modes in the gap. Conditions for theparadoxical appearance of the forerunning jet arerevealed to have a geometrical nature as a specificrelation between phase and group velocities involved.This deduction assigns the stated effect to thecounterintuitive manifestation of causality with noreference to superluminal propagation.

Propagation of auto-focusing Hypergeometric Gaussian beams along a slant Path in oceanic turbulence

Wenhai Wang, Zhou Yu, Chengzhao Liu, Xu Zhou, Zhengda Hu, and Yun Zhu

DOI: 10.1364/JOSAA.519982 Received 25 Jan 2024; Accepted 02 Apr 2024; Posted 02 Apr 2024  View: PDF

Abstract: Compared to horizontal transmission, the oceanic dissipation rate and temperature-salinity distribution ratio are no longer constant but vary with depth, imposing greater complexity on oceanic turbulence when beams propagate through a slant path and resulting in more limitations on the performance of underwater wireless optical communication (UWOC) links. This study focuses on investigating the performance, especially the auto-focusing characteristic, of auto-focusing Hypergeometric Gaussian (AHGG) beams propagating along slant paths in oceanic turbulence. We theoretically derive the spatial coherence radius and the relative probability of the orbital angular momentum (OAM) mode for AHGG beams passing through such links. Numerical simulations reveal that AHGG beams exhibit superior propagation performance compared to Hypergeometric Gaussian beams. Lower beam orders and OAM numbers contribute to improved performance, while careful selection of autofocusing length can tangibly enhance detection performance as well. Additionally, tidal velocities and wind speeds have non-negligible effects on OAM signal probability. Our results further demonstrate that surface buoyancy flux, temperature gradients, and waterside friction velocity significantly affect beam transmission under varying wind conditions. These findings, particularly controlling the autofocusing length of AHGG beams to match the transmission distance, provide valuable insights for enhancing the quality of UWOC links.

Projected algebraic reconstruction techniquenetwork for high- fidelity diffuse fluorescence tomography reconstruction

Wenjing Sun, Limin Zhang, Lingxiu Xing, Zhuanxia He, Yanqi Zhang, and Feng Gao

DOI: 10.1364/JOSAA.517742 Received 04 Jan 2024; Accepted 01 Apr 2024; Posted 02 Apr 2024  View: PDF

Abstract: We propose a model-driven projected algebraic reconstruction technique (PART)-network (PART-Net) that leverages the advantages of the traditional model-based method andthe neural network to improve imaging quality of diffuse fluorescence tomography (DFT). Inthis algorithm, non-negative prior information is incorporated into the ART iteration processto better guide the optimization process, and thereby improve imaging quality. On this basis,PART in conjunction with residual convolutional neural network is further proposed to obtainhigh fidelity image reconstruction. The numerical simulation results demonstrate that thePART-Net algorithm effectively improves noise robustness and reconstruction accuracy by atleast 1-2 times, and exhibits superiority in spatial resolution and quantification, especially forsmall-sized target (r mm = 2 ), compared with the traditional ART algorithm. Furthermore,the phantom and in vivo experiments verify the effectiveness of the PART-Net, suggestingstrong generalization capability and a great potential for practical applications.

Effect of an aperture in atomic gravimetry

Juan Cervantes and Eduardo Gomez Garcia

DOI: 10.1364/JOSAA.503050 Received 17 Oct 2023; Accepted 29 Mar 2024; Posted 01 Apr 2024  View: PDF

Abstract: There is a continuous interest in shrinking the dimensions of portable atomic gravimeters. This inevitably ends up truncating the Gaussian wings of the excitation laser beams whose effect has not been properly quantified yet. The diffraction pattern created from this aperture creates ripples in the wavefront both in the phase and intensity. We calculate the shift in the measured value of an atomic gravimeter introduced by the phase variations in the wavefront. Fortunately this shift has a Gaussian decay with the aperture size. For extended clouds, we observe a reduction of the effect thanks to an averaging over transverse positions with different values of the shift. Surprisingly, we found that the intensity variations also introduce an important correction to the photon recoil, which contributes at about the same level as the previous shift in the measurement of the gravitational acceleration. Our results should help deciding how small an apparatus can be to guarantee a particular accuracy.

Archimedes Spiral beam: Composite of helical-axicon generated Bessel beam and Gaussian beam

Zhoulin Ding and Yongji Yu

DOI: 10.1364/JOSAA.520541 Received 31 Jan 2024; Accepted 27 Mar 2024; Posted 29 Mar 2024  View: PDF

Abstract: This paper introduces a structured beam with Archimedes spiral intensity distribution. Archimedes spiral (AS) beam is the composite of a helical-axicon generated (HAG) Bessel beam and a Gaussian (GS) beam. We observed the spiral intensity patterns using computational holography, achieving the tuning over spiral arms number and spiral spacing. Analyzing the propagation dynamics of AS beams, we present that the spiral intensity will reverse beyond the maximum diffraction-free distance. Before and after the beam reverse, the spiral spacing remains constant, but the spiral direction is opposite. In addition, we obtain the Archimedes spiral equations to describe the spiral intensity patterns. Unlike the beams with Fermat and hyperbolic spiral patterns, the intensity distributions of AS beams are isometric spiral. The isometric spiral intensity makes it possible to form particle isometric channels. AS beams have potential application prospects in particle manipulation, microscopic imaging and laser processing.

Synthesizing Polarization Singularity Lattices Using Phase Ramps

KAPIL GANGWAR, Sarvesh Bansal, and Paramasivam Senthilkumaran

DOI: 10.1364/JOSAA.521031 Received 07 Feb 2024; Accepted 27 Mar 2024; Posted 29 Mar 2024  View: PDF

Abstract: In this paper, a novel methodology for generating polarization singularity lattices using ramp phase structures in a polarization interferometer is presented. By applying differential tilts to distinct regions within the wavefront using a spatial light modulator, a phase-discontinuity line separating the two regions is formed. During propagation along this line, phase vortices are formed at discrete points about which the phase difference on either side of the ramp is π. This wavefront with phase vortices is superimposed with a plane wave in orthogonal polarization in a polarization interferometer, giving rise to polarization singularities. A common-path polarization interferometer is constructed using a spatial light modulator to reduce errors and complexity. Polarization fringes instead of intensity fringes obtained in this interferometer host polarization singularities. Lattices made up of a linear chain of polarization singularities—unusually of the same index polarity—are found here. Experimental results corroborate the theoretical predictions. This study shows that singularities can be produced with non-spiral phase plates by using linear phase ramps. The method discussed in this manuscript may find potential applications in optical trapping and particle steering.

First Experimental Investigation on Backscattering Interference Cancellation for Full-duplex UOWC Based on Time-reversal Preprocessing

Weijie Liu, Shuzhe Zhang, Nuo Huang, and Zhengyuan Xu

DOI: 10.1364/JOSAA.516949 Received 27 Dec 2023; Accepted 26 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: A co-frequency and full-duplex (FD) underwater optical wireless communication (UOWC) system hasthe potential to significantly enhance spectral efficiency, reduce complexity, and further facilitate UOWCnetworking. However, the inevitable performance degradation due to self-interference introduced bybackscattering presents a significant challenge. In this paper, we first experimentally explore the inherent characteristics of the underwater backscattering channel. Subsequently, we propose a digitaldomain backscattering interference cancellation (BIC) algorithm for FD-UOWC systems, incorporating atime-reversal preprocessing. We then experimentally investigate the communication performance of anFD-UOWC system to verify the feasibility of the proposed BIC algorithm under different channel conditions. The experimental results validate the effectiveness of the proposed method, yielding substantialenhancements in bit error rate performance across diverse scenarios.

Fluorescence Molecular Tomography Based on Online Maximum a Posteriori Estimation Algorithm

Xia Cheng, Siyu Sun, Yinglong Xiao, Wenjing Li, Jintao Li, Jingjing Yu, and Guo hongbo

DOI: 10.1364/JOSAA.519667 Received 26 Jan 2024; Accepted 25 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: Fluorescence Molecular Tomography (FMT) is a noninvasive, radiation-free, and highly sensitive opticalmolecular imaging technique for early tumor detection.However, inadequate measurement information alongwith significant scattering of near-infrared light withinthe tissue leads to high ill-posedness in the inverseproblem of FMT. To improve the quality and efficiency ofFMT reconstruction, we build a reconstruction modelbased on Log-sum regularization and introduce an OnlineMaximum a Posteriori Estimation (OPE) algorithm tosolve the non-convex optimization problem. The OPEalgorithm approximates a stationary point by evaluatingthe gradient of the objective function at each iteration, andits notable strength lies in the remarkable speed ofconvergence. The results of simulations and experimentsdemonstrate that the OPE algorithm ensures goodreconstruction quality and exhibits outstandingperformance in terms of reconstruction efficiency.

Advanced Linear Axial Wavelength Spreading through Cascaded Double Hyperchromats

Lukas Werner, Hartmut Hillmer, and Robert Brunner

DOI: 10.1364/JOSAA.521502 Received 12 Feb 2024; Accepted 25 Mar 2024; Posted 25 Mar 2024  View: PDF

Abstract: This study explores the design and optimization of cascaded double-hyperchromatic optical systems (i.e. 2 x 2 lenses), focusing on achieving an extremely linear axial spectral decomposition characterized by an exceptionally low equivalent Abbe number. The investigation involves two double hyperchromats, considering both purely refractive systems and hybrid configurations that combine refractive and diffractive elements. For purely refractive systems, alternating focal lengths signs of divergent and collective lenses are crucial to achieve significant axial chromatic dispersion. In hybrid systems, the position of the Diffractive Optical Element (DOE) and the selection of focal lengths play key roles in obtaining extremely low equivalent Abbe numbers. The optimized systems demonstrate absolute equivalent Abbe numbers of 0.983 for purely refractive and 0.65 for hybrid systems—more than four times lower than the absolute Abbe number of a single diffractive element. Notably, even systems using standard materials exhibit significantly low equivalent Abbe numbers of 2.5 and 1.4 for pure refractive and hybrid configurations, respectively. These results offer promising opportunities for improving optical applications based on axial spectral decomposition, overcoming previous limitations of axial chromatic spreading.

Quaternion fast and accurate polar harmonic Fourier moments for color images analysis and object recognition

Si Yang and Ansheng Deng

DOI: 10.1364/JOSAA.514567 Received 01 Dec 2023; Accepted 24 Mar 2024; Posted 25 Mar 2024  View: PDF

Abstract: Image moments, as a kind of global feature descriptor ofimages, have become a valuable tool for pattern recognition and image analysis. However, traditional methodsare mainly used to deal with grayscale images. In thispaper, we apply quaternions to fast and accurate polarharmonic Fourier moments, proposing a kind of quaternion fast and accurate polar harmonic Fourier moments(QFAPHFMs) capable of handling color images. Furthermore, this paper provides a detailed analysis of theinvariance of QFAPHFMs under rotation, scaling, andtranslation transformations. The experimental resultsshow that QFAPHFMs exhibits excellent performance inboth image reconstruction and object recognition tasks.QFAPHFMs achieve accurate image reconstruction under noiseless and noisy conditions, and demonstrateexcellent recognition performance in the color-basedobject recognition task.

Minimizing Optical Attribute Errors for Lane Departure Warning System Using Ultra-Wide Angle Camera

Hyungtae Kim and Joonki Paik

DOI: 10.1364/JOSAA.495368 Received 11 May 2023; Accepted 23 Mar 2024; Posted 25 Mar 2024  View: PDF

Abstract: Advanced Driver Assistance Systems (ADAS) rely on Lane Departure Warning(LDW) technology to enhance safety while driving. However, the current LDW method islimited to cameras with standard angles of view, such as mono cameras and black boxes. Inrecent times, more cameras with ultra-wide-angle lenses are being used to save money andimprove accuracy. However, this has caused some problems such as fixing optical distortion,making the camera process images faster, and ensuring its performance. To effectively implementLDW, we developed three technologies: i) distortion correction using error functions based onthe projection characteristics of optical lenses, ii) automatic vanishing point estimation usinggeometric characteristics, and iii) lane tracking and lane departure detection using constraints. Theproposed technology improves system stability and convenience through automatic calculationand updating of parameters required for LDW function operation. By performing automatic distortion correction and vanishing point estimation, it has also been proven that fusion withother ADAS systems including front cameras is possible. Existing systems that use vanishingpoint information do not consider lens distortion and have slow and inaccurate vanishing pointestimation, leading to a deterioration of system performance. The proposed method enables fastand accurate vanishing point estimation, allowing for adaptive responses to changes in the roadenvironment.

Tutorial: Nonlinear Ray Tracing in Focused Fields. Part 3: Monochromatic Wavefront Aberration

qin yu and Bryan Hennelly

DOI: 10.1364/JOSAA.503924 Received 29 Aug 2023; Accepted 22 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: Using the flux tracing algorithm developed in the previous two parts, we examine the nonlinear rays that pass through the focus of a lens containing monochromatic aberrations. Lens aberration is modeled differently in the numerical propagation algorithms relating to the thin lens and the ideal lens case. For the former, an additive phase term is applied to the transmission function of the thin lens, which describes a distortion in the thickness function of the lens, and for the latter an additive phase term is added to the pupil function of the lens (the Fourier transform of the image plane). In both cases, the Zernike polynomials are applied to model various aberrations including spherical, defocus, comatic, astigmatism, trefoil, and quadrafoil. Despite the different methods of modelling aberration for the two types of lens, remarkably similar results are obtained for both cases. A discussion is also provided on the relation ship between classical wavefront aberration theory and nonlinear tracing. This paper demonstrates the extraordinary potential of nonlinear ray tracing to gain insights into complex optical phenomena.

Tutorial: Nonlinear Ray Tracing in Focused Fields. Part 2: Tracing the Flux.

Bryan Hennelly and qin yu

DOI: 10.1364/JOSAA.503925 Received 29 Aug 2023; Accepted 22 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: In this three part paper, we develop a method to trace the lines of flux through a three-dimensional wavefield by following a direction that is governed by the derivative of the phase at each point, a process that is best described as flux tracing but which we interchangeably name as 'nonlinear ray tracing'. In the first part we focused on the high-speed calculation of focused three-dimensional complex wavefields in the paraxial approximation for TEM00 and TEM01 laser modes. The algorithms developed in the first paper are first used to generate the three-dimensional grid of samples of the complex wavefield in the focal region. In this second part, we focus on tracing a flux through this three-dimensional point cloud. For a given 'ray' at an arbitrary position in the 3D volume, interpolation of the three-dimensional samples is applied to determine the derivative of the phase (normal to the direction of propagation) at the ray position, which is then used to direct the ray as it 'propagates' forward in a straight line over a short distance to a subsequent plane; the process is repeated between consecutive planes. The initial origin of the ray can be chosen arbitrarily at any point and the ray can be then be traced through the volume with appropriate interpolation. Results are demonstrated for focused wavefields in the absence of aberrations, corresponding to the cases highlighted in the first paper. Some of the most interesting results relate to focused Laguerre-Gaussian beams, for which the rays are found to spiral at different rates of curvature. In the third paper we extend the application of this algorithm to the investigation of lens aberration.

Tutorial: Nonlinear Ray Tracing in Focused Fields. Part 1: Calculating 3D Complex Wavefields.

qin yu and Bryan Hennelly

DOI: 10.1364/JOSAA.503926 Received 30 Aug 2023; Accepted 22 Mar 2024; Posted 26 Mar 2024  View: PDF

Abstract: In this three part paper, we develop a method to trace the lines of flux through a three-dimensional wavefield by following a direction that is governed by the derivative of the phase at each point, a process that is best described as flux tracing but which we interchangeably name as ’nonlinear ray tracing’. In this first part, we focus on the high-speed calculation of three-dimensional complex wavefields, which is a necessary precursor to flux tracing. The basis of this calculation is the Angular Spectrum method, a well known numerical algorithm that can be used to efficiently and accurately calculate diffracted fields for numerical apertures <0.7. It is known that this approach yields identical predictions to the first Rayleigh-Sommerfeld solution. We employ the Angular Spectrum method to develop two algorithms that generate the 3D complex wavefield in the region of focus of a lens. The first algorithm is based on the thin lens approximation and the second is based on the concept of an ideal lens, which can be modelled using an optical Fourier transform. Both algorithms are investigated to calculate focused laser beams with TEM00 and TEM01 laser profiles. The three-dimensional sampling requirements of the focused field are investigated in addition to the computational and memory efficiency of the two algorithms. These two algorithms generate the 3D scaffold for the flux tracing method developed in the second paper and in the third paper we highlight the application of the method to understanding monochromatic lens aberration. Disregarding the second and third papers, the two algorithms developed in this paper are interesting for anyone seeking to compute focused fields in three-dimensions.

Relationship between Turbulent Image Variance and Average Image Gradient

Guy Potvin

DOI: 10.1364/JOSAA.516238 Received 18 Dec 2023; Accepted 21 Mar 2024; Posted 21 Mar 2024  View: PDF

Abstract: Optical turbulence can cause substantial distortions in imaging over long horizontal paths.For Lambertian objects, these distortions are only seen where there is a gradient in the object's radiance.It is possible to establish a relationship between the intensity variance of a turbulent image and the average image's gradient squared.We test the validity of a linear relationship between these quantities using turbulent imaging data.We find that it performs reasonably well for weak and intermediate optical turbulence regimes, but that some discrepancies remain to be explained.The linear relationship may permit the determination of turbulence parameters using imaging data.

Virtually Measuring Layered Material Appearance

Kewei XU, Arthur cavalier, Benjamin Bringier, Mickaël Ribardière, and Daniel Meneveaux

DOI: 10.1364/JOSAA.514604 Received 30 Nov 2023; Accepted 17 Mar 2024; Posted 18 Mar 2024  View: PDF

Abstract: This paper describes the design and the implementation of a virtual gonioradiometer dedicated to theanalysis of layered materials BSDF. For a given material sample, interfaces between layers are representedby geometric meshes, associated with elementary reflectances. Light scattering is performed using pathtracing. Our system is composed of 5 hemispherical sensors, which cells have uniform solid angles, anda close-to-uniform geometry. The upper hemisphere captures the reflected radiance distribution, whilethe other 4 collect the light energy lost by the sample sides. Sensor resolutions can be set to gather veryfine details of the BSDF. With the proposed system, any type of virtual surface reflection and transmissioncan be simulated, with several controllable surface layers, and with any type of reflection configuration,including direct reflections, two bounces of reflection, or all contributions. A series of results are providedwith several types of layered materials, as well as discussion and analysis concerning the assumptionsmade with analytical layered BSDF models. We also propose an in-depth study of the side effects thatinevitably appear when measuring such (real) material configurations. Finally, our system will be freelyavailable to the community (open source dissemination). ©